Linear Algebra - Fall 2000

COURSE: MATH 2250-001

TIME: 10:25-11:20 MWF PLACE: 205 Gilbreath Hall

INSTRUCTOR: Dr. Robert Gardner, OFFICE: 308G Gilbreath Hall

OFFICE HOURS: 1:40-2:35 MWF, PHONE: 439-6977 (Math Office 439-4349)

OTHER OFFICE: Room 201 of Brown Hall (the Institute of Mathematical and Physical Sciences), phone 439-8684.

E-MAIL ADDRESS: gardnerr@etsu.edu.

HOMEPAGE: www.etsu.edu/math/gardner/gardner.htm (see my homepage for a copy of this course syllabus and updates for the course).

ON-LINE COURSE NOTES:Lecture notes are available on the web at:

http://www.etsu.edu/math/gardner/2250/notes.htm

TEACHING ASSISTANT: Scott Lavoie OFFICE: TBA OFFICE HOURS: TBA

TEXT: Linear Algebra, Ideas and Applications, by R. C. Penney.

SUPPLEMENTAL TEXTS: (each is on reserve in the library):

  1. Student Resource Manual to Accompany "Linear Algebra, Ideas and Applications," by R. C. Penney. Contains more worked out examples, further hints for some of the exercises, and translations of the computer exercises into various platforms.
  2. Instructor's Resource Manual to Accompany "Linear Algebra, Ideas and Applications," by R. C. Penney. This includes solutions to ALL problems in the text (including the "on line" exercises).

PREREQUISITES: MATH 1060, MATH 1032, or MATH 1110. You need to be knowledgable of differential calculus.

ABOUT THE COURSE: Linear Algebra (or "Matrix Theory") is one of the most useful areas of mathematics. It is applicable in mathematics itself in areas ranging from Calculus and Discrete Math to Functional Analysis. It is applicable in statistics (least-squares methods and transition matrices), biology (population distributions and genetics), physics (theoretical and applied), computer science (in coding theory and cryptography) and almost any other area that uses numbers! We will try to illustrate some of these applications in this class.

GRADING: We will have four tests (T1, T2, T3 and T4) and a comprehensive final (F). Your average will be computed as follows:

AVERAGE = (T1 + T2 + T3 + T4 + 2F)/6.
Grades will be assigned based on a 10 point scale with "plus" and "minus" grades being assigned as appropriate.

MATH LAB: The Mathematics Laboratory is located in Rooms 308 and 309 of Warf-Pickle Hall. It is staffed by graduate students and upper level undergraduates. They are there to help you! They are there to help you! Hours of operation are (tentatively) Monday--Thursday 11:30--7:30, Sunday 1:30--5:30. The phone number is 439-5968. The Math Hotline is 439-8586 (for short questions).

A NOTE ABOUT TECHNOLOGY: Since we are in the Department of Mathematics' "Technology Classroom," we will use the software MATLAB to do some of our computational work. "In principle, the instructor should not need to spend any class time at all discussing computing" [Penney, page viii]. None-the-less, we will set aside two classdays before the first test specifically to discuss MATLAB commands. After that, the use of MATLAB will be woven into the lectures.

A NOTE ON TESTS: For a portion of each test, you will not be allowed to use calculators or computers. This part of the test will include questions about definitions, proofs and elementary computations.

IMPORTANT DATES:

Tentative Outline

DATE AGENDA HOMEWORK
MON 8/28 1.1 = intro, vectors 1.1 = 1-21 odd
WED 8/30 1.1 (cont.), 1.2 = vector spaces of matrices 1.2 = 1-27 odd
FRI 9/1 1.2 (cont.) -
MON 9/4 Labor Day Holiday -
WED 9/6 MATLAB day -
FRI 9/8 1.3 = linear equations 1.3 = 1-11 odd
MON 9/11 1.3 (cont.), 1.4 = Gaussian elimination 1.4 = 1-17 odd
WED 9/13 1.4 (cont.) -
FRI 9/15 1.4 (cont.), 1.5 = column and nullspace 1.5 = 1-33 odd
MON 9/18 1.5 (cont.) -
WED 9/20 MATLAB day -
FRI 9/22 review -
MON 9/25 TEST 1 (1.1-1.5) -
WED 9/27 2.1 = linear independence 2.1 = 1-13 odd
FRI 9/29 2.2 = dimension 2.2 = 1-31 odd
MON 10/2 2.2 (cont.), 2.3 = applications of systems 2.3 = 1-17 odd
WED 10/4 2.3 (cont.)
FRI 10/6 3.1 = matrix transformations 3.1 = 1-27 odd
MON 10/9 3.1 (cont.), 3.2 = matrix multiplication 3.2 = 1-27 odd
WED 10/11 3.2 (cont.) -
FRI 10/13 3.3 = image of a transformation 3.3 = 1-21 odd
MON 10/16 review -
WED 10/18 TEST 2 (2.1-3.2) -
FRI 10/20 3.4 = inverse matrices 3.4 = 1-31 odd
MON 10/23 3.4 (cont.), 4.1 = coordinates 1-13 odd
WED 10/25 4.1 (cont.) -
FRI 10/27 Fall Break (no class) -
MON 10/30 4.2 = Gram-Schmidt process 4.2 = 1-17 odd
WED 11/1 4.2 (cont.), 4.4 = orthogonal matrices 4.4 = 1-13 odd
FRI 11/3 4.4 (cont.) -
MON 11/6 4.5 = least squares 4.5 = 1-19 odd
WED 11/8 review -
FRI 11/10 TEST 3 (3.3-4.2, 4.4, 4.5) -
MON 11/13 5.1 = determinants 5.1 = 1-11 odd
WED 11/15 5.1 (cont.), 5.2 = reduction and determinants 5.2 = 1-15 odd
FRI 11/17 5.2 (cont.) -
MON 11/20 6.1 = eigenvectors 6.1 = 1-17 odd
WED 11/22 6.1 (cont.), 6.2 = diagonalization 6.2 = 1-17 odd
FRI 11/24 Thanksgiving Holiday -
MON 11/27 6.2 (cont.) -
WED 11/29 review -
FRI 12/1 TEST 4 (5.1-6.2) -
MON 12/4 6.5 = orthogonal diagonalization 6.5 = 1-15 odd
WED 12/6 6.5 (cont.) -
FRI 12/8 review -
WED 12/13 COMPREHENSIVE FINAL 8:00-10:00 -

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